IMHO, and with respect, poker results have a very high variance which may yet overwhelm your good results.

According to back of an envelope calculation, if there was no skill in poker, and you were just coin flipping, approximately 1 player for every 28 would come out with similar results.

This is a statistically significant result, I suppose, but not very. There are presumably many thousands of players who can present similar results, whether or not they have any skill. The jury's still out over whether you can continue this streak and claim +EV in the long term.

You should have some serious concern about this, since you are subject to self-selection bias in posting these results.

All-in-all, your results don't yet convince me that poker is a skill game, or at least not (yet) that you are skilled. Get back to me after the next 18,000 games, if you feel like it.

I confess to some dubious assumptions but I tend to believe that those assumptions averaged in your favour. This perhaps illustrates why poker is so good at hooking people.

Without double checking your math, I'm pretty sure the significant error in your conclusion here is modeling the games he's playing as coin flipping with even payouts. The specific game he's playing is actually dropping a percentage each time and is more accurately modeled as "heads I win .98, tails I lose 1". (Technically he's betting $15 for a chance to win $14.69). With that in mind, many fewer than 1 in 28 players would end up with his results.

Typically in poker, you win quickly and lose slowly. This is especially true of tournaments - finishing in the money suddenly does wonders for your balance.

So, I would guess that more than 1 in 28 players would show these results, having experienced a random "win quickly" phase that has yet to dissipate.

(This might not apply if parent is talking only about 2 player tournaments, but applies to poker generally)

Parent is talking only about 2 player tournaments - that's what the "heads up" part of the description means.

OK, I getcha, thanks.

Heads Up specifically means that there are match-ups between 2 players. This doesn't mean it's necessarily a 2 player tournament, e.g.

https://en.wikipedia.org/wiki/National_Heads-Up_Poker_Champi...

I already checked this case and you are right, indeed.

Yes, sorry, I should have specified that each buy-in has a small percentage raked from it which goes to PokerStars for hosting the game.

Rake is a part of every form of real money poker. It's how casinos and online poker sites make their $$$'s.

You are absolutely correct that poker results have high variance but you only need a sample of around 5000 matches or so before your results begin to closely depict your true winrate. I only showed an image of my $15 heads-up hyper-turbos on PokerStars. Below is a link to my graph for all heads-up hyper-turbos I've played over my life, 50k+. This graph shows my play from the $1.50 games all the way up to the $200 games. If you didn't trust in a 18k sample, maybe this 50k sample will help sway your opinion.

http://i.imgur.com/1uC5y0U.png

Note that I'm also only a mediocre regular in these games. There are MANY people who have far better results than I do. They average a 3-5% ROI which is much higher than mine.

Also note that the reason my graph dipped after the first 10k games or so was because I went from playing the $15s-$30s to playing the $100s/$200s for awhile. Due to the increased skill level I dropped back down. Here's another image showing my stats for each buy-in level.

http://i.imgur.com/D0lHx3H.png

If you still doubt how confident you can be in this sample, you might want to read the following article on confidence intervals on husng.com:

http://www.husng.com/content/given-my-results-what-should-my...

My 50k+ game sample means that there is a far lower than 0.1% chance that my results are due to the good end of variance.

And here's a graph of ALL my poker tournaments. This includes 9-handed multi-table tournaments, 6-handed SNGs, heads-up shootouts, everything.

http://i.imgur.com/6jyCXn0.png

Poker is 100% a game of skill but it really depends on how you approach it. Professional players or serious amateurs such as myself make money at the game simply because people approach it as if it's bingo.

If every recreational player was putting in time studying poker theory and reviewing their play, it would become much, much harder to make money playing. As such, I really don't mind if people want to continue thinking it's a luck based thing. It just means more profit for me since that perspective, oddly enough, doesn't stop people from dropping $$$ in the game, it merely stops them from thinking they can gain an edge by putting in time and effort. Recreational players wouldn't play if there wasn't a certain amount of luck...

EDIT: Also, it's important to note that every poker player has to pay for their education. Look at my last graph. I was an unprofitable player for the first 10-20 thousand games or so. That was when I was just playing micro/low stakes on PokerStars recreationally. Once I gained some knowledge, and decided to take it much more seriously, my profits skyrocketed.

It's far better to learn how to play poker at micro/low stakes online, where you will pay less for your poker education, than it is to start with mid/high stakes online or in your local casino. Either way, you'll be a losing player to start. Choose the more inexpensive option.

I genuinely have some concerns about what you're saying - I believe you need to try to look at the stats critically or conservatively, without the influence of poker marketing itself to players.

You're saying that 5,000 games is enough to determine your overall winrate, and yet every 5,000 games of yours has been different: from game 31,000 to 50,000 (a recent 19,000 game streak), you are down.

Either this should mean you are a losing player, or it means 20,000 games is not even nearly enough to draw a conclusion. Be careful about having it both ways to suit you: that is confirmation bias https://en.wikipedia.org/wiki/Confirmation_bias.

Let's say, I wish you the best of luck, and leave it at that.

Good luck :)

I said after 5,000 games your results will begin to closely depict your winrate, not that it would 100% be correct. Variance can easily cause a winning player to have a breakeven stretch.

On top of that, you seem to be suggesting that the variance in my ROI is somehow attributed to an inherent "luck" factor of poker while ignoring the fact that the sample size ranges from micro stakes up to high stakes poker. My winrate is obviously going to vary between stakes because poker is a game of skill and the higher the limit, the more skilled the player pool.

FYI, it's also quite annoying to throw wikipedia pages explaining common psychological biases at me when you've already stated that you are basing most of your conclusions on "assumptions" since you aren't well acquainted with the subject matter. I'm well aware of everything you're warning me about but you also seem biased against poker. I've shown you a sample of over 50,000 tournaments. That's over 1.5 MILLION hands of poker. It blows my mind that you seem to be keen on ignoring empirical evidence and mathematical analysis here, but if you want to ignore that, so be it.

But, yes, indeed, good luck to you as well.